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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 346560dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.dc4 | 346560dc1 | \([0, -1, 0, 84941375, -1808469396383]\) | \(5495662324535111/117739817533440\) | \(-1452061083471690271461212160\) | \([2]\) | \(154828800\) | \(3.8922\) | \(\Gamma_0(N)\)-optimal |
| 346560.dc3 | 346560dc2 | \([0, -1, 0, -1807738305, -28020947356575]\) | \(52974743974734147769/3152005008998400\) | \(38873032966731898707089817600\) | \([2, 2]\) | \(309657600\) | \(4.2388\) | |
| 346560.dc2 | 346560dc3 | \([0, -1, 0, -5400872385, 117958748165217]\) | \(1412712966892699019449/330160465517040000\) | \(4071801479920161210299842560000\) | \([2]\) | \(619315200\) | \(4.5854\) | |
| 346560.dc1 | 346560dc4 | \([0, -1, 0, -28497479105, -1851629515205535]\) | \(207530301091125281552569/805586668007040\) | \(9935135576751003664971202560\) | \([2]\) | \(619315200\) | \(4.5854\) |
Rank
sage: E.rank()
The elliptic curves in class 346560dc have rank \(0\).
Complex multiplication
The elliptic curves in class 346560dc do not have complex multiplication.Modular form 346560.2.a.dc
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
